OFFSET
0,5
COMMENTS
The sequence may increase when n is the sum of two squares (A001481).
An optimal polygon will always be convex. - Gordon Hamilton
For parity reasons, the edges of the maximal-area polygon are not always as long as possible. This is true for a(9) through a(12). - Gordon Hamilton
This puzzle sequence could be used when introducing students to slopes.
Are these values known to be optimal or are they conjectures? - N. J. A. Sloane, Mar 13 2015
These values have not been proved to be optimal.
EXAMPLE
a(4) = 2 because this triangle has area 1 (remember a(n) is twice the area):
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a(5) = a(6) = a(7) = 36 because of this polygon of area 18:
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a(8) = 50 because of this polygon of area 25:
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a(9) = 53 because of this polygon of area 26.5:
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. x . . . . . . .
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a(10) = 153 because of this polygon of area 76.5:
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. . . x . . x . . . . . .
. . x . . . . . x . . . .
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. x . . . . . . . . x . .
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. . x . . . . . x . . . .
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CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gordon Hamilton, Mar 13 2015
STATUS
approved